tut10_soln - Math 235 Tutorial 10 Problems —1 2 ~2 1...

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Unformatted text preview: Math 235 Tutorial 10 Problems —1 2 ~2 1: Diagonalize A = ——2 —1 —1 over (3. 4 —2 5 2: Prove that if _23' is an eigenvector of a matrix A with complex entries, then 5' is an eigenvector of A. What is the corresponding eigenvalue? 3: Suppose that a real 2 X 2 matrix A has 1 +2' as an eigenvalue with a corresponding 2 . ]. Determine A. eigenvector [ z 4: Let V be a real vector space. A complex structure on V is a real linear mapping J : V —> V satisfying J 2 = —Id where Id is the identity mapping. Prove that under the addition operation of V and scalar multiplication defined by (a + bib—3' = of + bJ(EE) for all a + bi E (C and if E V, that V becomes a complex vector space. r g 2 Qty?“ \J «\V Q {:3 x Sthlk‘ {2m\ \ (M! Mr ‘ j Hf- min} {0+5} \7 2 0‘3! Jr EELS) \L‘tfi Ema» 9) \/ \‘§\L) 3 {Ex ‘1 Ch) S‘t, {a ML m (\A‘S’) ’ v: 1R2 “'5: (gm, 5 70 (fig Q: (XE: (IND {‘33 C+§LJ\ " @+‘s\«>)i (mafia J 3(2)] 3 a a: + mi 375:2) «um T(:)+\~J“SD?I:) s: (“A”) )5: a, (ame’forg) ...
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